The direction cosines of a normal to the plane `2x-3y-6z+14=0` are (A) `(2/7,(-3)/7,(-6)/7)` (B) `((-2)/7,3/7,6/7)` (C) `((-2)/7,(-3)/3,(-6)/7)` (D) none of these

The direction cosines of the ray from (0,0,0) to (2,-3,6) are (A) -2/7,3/7,-6/7 (B) 2/7,37,6/7 (C) -2/7,-3/7,6/7 (D) 2/7,-3/7,6/

If projections of as line on x,y and z axes are 6,2 and 3 respectively, then directions cosines of the lines are (A) (6/2,2/7,3/7) (B) (3/5,5/7,6/7) (C) (1/7,2/7,3/7) (D) none of these

The reflection of the point (2,-1,3) in the plane 3x-2y-z=9 is (A) (28/7,15/7,17/7) (B) (26/7,-15/7,17/7) (C) (15/7,26/,-17/7) (D) (26/7,17/7,-15/70)

The distasnce of the plane 2x-3y+6z+14=0 from the origin is (A) 2 (B) 4 (C) 7 (D) 11

O is origin and P is a point at a distance of 7 units from origin if the direction ratios of OP are lt 3 ,-2, 6 gt , then the coordinates of P are (i) (3,-2,6) (ii) (21,-14,42) (iii) (3/7,-2/7,6/7) (iv) none of these

The distance between the parallel planes x+2y-3z=2 and 2x+4y-6z+7=0 is (A) 1/sqrt(14) (B) 11/sqrt(56) (C) 7/sqrt(56) (D) none of these

The inverse of the matrix [(2,3),(-4,7)] is (A) [(-2,-3),(4,-7)] (B) 1/26 [(7,-3),(4,2)] (C) [(7,4),(-3,2)] (D) [(7,-3),(4,2)]

The equation of the parallel plane lying midway between the parallel planes 2x-3y+6z-7=0 and 2x-3y+6z+7=0 is (A) 2x-3y+6z+1=0 (B) 2x-3y+6z-1=0 (C) 2x-3y+6z=0 (D) none of these

The projections of a vector on the three coordinate axis are 6, 3, 2 respectively. The direction cosines of the vector are (A) 6,-3,2 (B) 6/5,(-3)/5,2/5 (C) 6/7,(-3)/7,2/7 (D) (-6)/7,(-3)/7,2/7

The line (x+6)/5=(y+10)/3=(z+14)/8 is the hypotenuse of an isosceles right-angled triangle whose opposite vertex is (7,2,4)dot Then which of the following is not the side of the triangle? a. (x-7)/2=(y-2)/(-3)=(z-4)/6 b. (x-7)/3=(y-2)/6=(z-4)/2 c. (x-7)/3=(y-2)/5=(z-4)/(-1) d. none of these